Ion conductance vs. pore gating and selectivity in KcsA channel: Modeling achievements and perspectives

Resonance-driven ion transport and selectivity in prokaryotic ion channels

Ion channels exhibit a remarkably high accuracy in selecting uniquely its associated type of ion. The mechanisms behind ion selectivity are not well understood. Current explanations build mainly on molecular biology and bioinformatics. Here we propose a simple physical model for ion selectivity based on the driven damped harmonic oscillator (DDHO). The driving force for this oscillator is provided by self-organizing harmonic turbulent structures in the dehydrating ionic flow through the ion channel, namely, oscillating pressure waves in one dimension, and toroidal vortices in two and three dimensions. Density fluctuations caused by these turbulences efficiently transmit their energy to aqua ions that resonate with the driving frequency. Consequently, these release their hydration shell and exit the ion channel as free ions. Existing modeling frameworks do not express the required complex spatiotemporal dynamics, hence we introduce a macroscopic continuum model for ionic dehydration and transport, based on the hydrodynamics of a dissipative ionic flow through an ion channel, subject to electrostatic and amphiphilic interactions. This model combines three classical physical fields: Navier-Stokes equations from hydrodynamics, Gauss's law from Maxwell theory, and the convection-diffusion equation from continuum physics. Numerical experiments with mixtures of chemical species of ions in various degrees of hydration indeed reveal the emergence of strong oscillations in the ionic flow that are instrumental in the efficient dehydration and cause a strong ionic jet into the cell. As such, they provide a powerful engine for the DDHO mechanism. Theoretical predictions of the modeling framework match significantly with empirical patch-clamp data. The DDHO standard response curve defines a unique resonance frequency that depends on the mass and charge of the ion. In this way, the driving oscillations act as a selection mechanism that filters out one specific ion. Application of the DDHO model to real ion data shows that this mechanism indeed clearly distinguishes between chemical species and between aqua and bare ions with a large Mahalanobis distance and high oscillator quality. The DDHO framework helps to understand how SNP mutations can cause severe genetic pathologies as they destroy the geometry of the channel and so alter the resonance peaks of the required ion type.

Modeling Electronic Polarizability Changes in the Course of a Magnesium Ion Water Ligand Exchange Process

This paper introduces explicit dependence of atomic polarizabilities on intermolecular interactions within the framework of a polarizable force field AMOEBA. Polarizable models used in biomolecular simulations often poorly describe molecular electrostatic induction in condensed phase, in part, due to neglect of a strong dependency of molecular electronic polarizability on intermolecular interactions at short distances. Our variable polarizability model parameters are derived from quantum chemical calculations of small clusters of atoms and molecules, and can be applied in simulations in condensed phase without additional scaling factors. The variable polarizability model is applied to simulate a ligand exchange reaction for a Mg(2+) ion solvated in water. Explicit dependence of water polarizability on a distance between a water oxygen and Mg(2+) is derived from in vacuum MP2 calculations of Mg(2+)-water dimer. The simulations yield a consistent description of the energetics of the Mg(2+)-water clusters of different size. Simulations also reproduce thermodynamics of ion solvation as well as kinetics of a water ligand exchange reaction. In contrast, simulations that used the additive force field or that used the constant polarizability models were not able to consistently and quantitatively describe the properties of the solvated Mg(2+) ion.

The open gate of the K(V)1.2 channel: quantum calculations show the key role of hydration

The open gate of the Kv1.2 voltage-gated potassium channel can just hold a hydrated K(+) ion. Quantum calculations starting from the x-ray coordinates of the channel confirm this, showing little change from the x-ray coordinates for the protein. Water molecules not in the x-ray coordinates, and the ion itself, are placed by the calculation. The water molecules, including their orientation and hydrogen bonding, with and without an ion, are critical for the path of the ion, from the solution to the gate. A sequence of steps is postulated in which the potential experienced by the ion in the pore is influenced by the position of the ion. The gate structure, with and without the ion, has been optimized. The charges on the atoms and bond lengths have been calculated using natural bond orbital calculations, giving K(+) ~0.77 charges, rather than 1.0. The PVPV hinge sequence has been mutated in silico to PVVV (P407V in the 2A79 numbering). The water structure around the ion becomes discontinuous, separated into two sections, above and below the ion. PVPV conservation closely relates to maintaining the water structure. Finally, these results have implications concerning gating.

Molecular modeling in structural nano-toxicology: interactions of nano-particles with nano-machinery of cells

Over the past two decades, nanotechnology has emerged as a key player in various disciplines of science and technology. Some of the most exciting applications are in the field of biomedicine - for theranostics (for combined diagnostic and therapeutic purposes) as well as for exploration of biological systems. A detailed understanding of the molecular interactions between nanoparticles and biological nano-machinery - macromolecules, membranes, and intracellular organelles - is crucial for obtaining adequate information on mechanisms of action of nanomaterials as well as a perspective on the long term effects of these materials and their possible toxicological outcomes. This review focuses on the use of structure-based computational molecular modeling as a tool to understand and to predict the interactions between nanomaterials and nano-biosystems. We review major approaches and provide examples of computational analysis of the structural principles behind such interactions. A rationale on how nanoparticles of different sizes, shape, structure and chemical properties can affect the organization and functions of nano-machinery of cells is also presented.

Voltage gated ion channel function: gating, conduction, and the role of water and protons

Ion channels, which are found in every biological cell, regulate the concentration of electrolytes, and are responsible for multiple biological functions, including in particular the propagation of nerve impulses. The channels with the latter function are gated (opened) by a voltage signal, which allows Na(+) into the cell and K(+) out. These channels have several positively charged amino acids on a transmembrane domain of their voltage sensor, and it is generally considered, based primarily on two lines of experimental evidence, that these charges move with respect to the membrane to open the channel. At least three forms of motion, with greatly differing extents and mechanisms of motion, have been proposed. There is a "gating current", a capacitative current preceding the channel opening, that corresponds to several charges (for one class of channel typically 12-13) crossing the membrane field, which may not require protein physically crossing a large fraction of the membrane. The coupling to the opening of the channel would in these models depend on the motion. The conduction itself is usually assumed to require the "gate" of the channel to be pulled apart to allow ions to enter as a section of the protein partially crosses the membrane, and a selectivity filter at the opposite end of the channel determines the ion which is allowed to pass through. We will here primarily consider K(+) channels, although Na(+) channels are similar. We propose that the mechanism of gating differs from that which is generally accepted, in that the positively charged residues need not move (there may be some motion, but not as gating current). Instead, protons may constitute the gating current, causing the gate to open; opening consists of only increasing the diameter at the gate from approximately 6 Å to approximately 12 Å. We propose in addition that the gate oscillates rather than simply opens, and the ion experiences a barrier to its motion across the channel that is tuned by the water present within the channel. Our own quantum calculations as well as numerous experiments of others are interpreted in terms of this hypothesis. It is also shown that the evidence that supports the motion of the sensor as the gating current can also be consistent with the hypothesis we present.

A permeation theory for single-file ion channels: one- and two-step models

How many steps are required to model permeation through ion channels? This question is investigated by comparing one- and two-step models of permeation with experiment and MD simulation for the first time. In recent MD simulations, the observed permeation mechanism was identified as resembling a Hodgkin and Keynes knock-on mechanism with one voltage-dependent rate-determining step [Jensen et al., PNAS 107, 5833 (2010)]. These previously published simulation data are fitted to a one-step knock-on model that successfully explains the highly non-Ohmic current-voltage curve observed in the simulation. However, these predictions (and the simulations upon which they are based) are not representative of real channel behavior, which is typically Ohmic at low voltages. A two-step association/dissociation (A/D) model is then compared with experiment for the first time. This two-parameter model is shown to be remarkably consistent with previously published permeation experiments through the MaxiK potassium channel over a wide range of concentrations and positive voltages. The A/D model also provides a first-order explanation of permeation through the Shaker potassium channel, but it does not explain the asymmetry observed experimentally. To address this, a new asymmetric variant of the A/D model is developed using the present theoretical framework. It includes a third parameter that represents the value of the "permeation coordinate" (fractional electric potential energy) corresponding to the triply occupied state n of the channel. This asymmetric A/D model is fitted to published permeation data through the Shaker potassium channel at physiological concentrations, and it successfully predicts qualitative changes in the negative current-voltage data (including a transition to super-Ohmic behavior) based solely on a fit to positive-voltage data (that appear linear). The A/D model appears to be qualitatively consistent with a large group of published MD simulations, but no quantitative comparison has yet been made. The A/D model makes a network of predictions for how the elementary steps and the channel occupancy vary with both concentration and voltage. In addition, the proposed theoretical framework suggests a new way of plotting the energetics of the simulated system using a one-dimensional permeation coordinate that uses electric potential energy as a metric for the net fractional progress through the permeation mechanism. This approach has the potential to provide a quantitative connection between atomistic simulations and permeation experiments for the first time.

Dynamics may significantly influence the estimation of interatomic distances in biomolecular X-ray structures

Atomic positions obtained by X-ray crystallography are time and space averages over many molecules in the crystal. Importantly, interatomic distances, calculated between such average positions and frequently used in structural and mechanistic analyses, can be substantially different from the more appropriate time-average and ensemble-average interatomic distances. Using crystallographic B-factors, one can deduce corrections, which have so far been applied exclusively to small molecules, to obtain correct average distances as a function of the type of atomic motion. Here, using 4774 high-quality protein X-ray structures, we study the significance of such corrections for different types of atomic motion. Importantly, we show that for distances shorter than 5 Å, corrections greater than 0.5 Å may apply, especially for noncorrelated or anticorrelated motion. For example, 14% of the studied structures have at least one pair of atoms with a correction of ≥0.5 Å in the case of noncorrelated motion. Using molecular dynamics simulations of villin headpiece, ubiquitin, and SH3 domain unit cells, we demonstrate that the majority of average interatomic distances in these proteins agree with noncorrelated corrections, suggesting that such deviations may be truly relevant. Importantly, we demonstrate that the corrections do not significantly affect stereochemistry and the overall quality of final refined X-ray structures, but can provide marked improvements in starting unrefined models obtained from low-resolution X-ray data. Finally, we illustrate the potential mechanistic and biological significance of the calculated corrections for KcsA ion channel and show that they provide indirect evidence that motions in its selectivity filter are highly correlated.

Conformational changes in the selectivity filter of the open-state KcsA channel: an energy minimization study

Potassium channels switch between closed and open conformations and selectively conduct K(+) ions. There are at least two gates. The TM2 bundle at the intracellular site is the primary gate of KcsA, and rearrangements at the selectivity filter (SF) act as the second gate. The SF blocks ion flow via an inactivation process similar to C-type inactivation of voltage-gated K(+) channels. We recently generated the open-state conformation of the KcsA channel. We found no major, possibly inactivating, structural changes in the SF associated with this massive inner-pore rearrangement, which suggests that the gates might act independently. Here we energy-minimize the open state of wild-type and mutant KcsA, validating in silico structures of energy-minimized SFs by comparison with crystallographic structures, and use these data to gain insight into how mutation, ion depletion, and K(+) to Na(+) substitution influence SF conformation. Both E71 or D80 protonations/mutations and the presence/absence of protein-buried water molecule(s) modify the H-bonding network stabilizing the P-loops, spawning numerous SF conformations. We find that the inactivated state corresponds to conformations with a partially unoccupied or an entirely empty SF. These structures, involving modifications in all four P-loops, are stabilized by H-bonds between amide H and carbonyl O atoms from adjacent P-loops, which block ion passage. The inner portions of the P-loops are more rigid than the outer parts. Changes are localized to the outer binding sites, with innermost site S4 persisting in the inactivated state. Strong binding by Na(+) locally contracts the SF around Na(+), releasing ligands that do not participate in Na(+) coordination, and occluding the permeation pathway. K(+) selectivity primarily appears to arise from the inability of the SF to completely dehydrate Na(+) ions due to basic structural differences between liquid water and the "quasi-liquid" SF matrix.